Is there any recourse if you fall behind on mortgage payments and the bank is requesting a relief of stay from the courts?

A secured lender (especially a mortgage holder) has a lot of leverage when collecting on the loan. If the stay is granted an the loan can be reaffirmed missed payments and penalties made up (plus regularly due payments), foreclosure is a certainty. It might be wise to let the house go in the bankruptcy, whereby you can collect your exemption and at least not lose your equity (investment) in foreclosure proceedings. State statutes differ in how foreclosure proceedures and/or bankruptcy homestead exemptions apply. If you have a decent attorney, they can normally put on some "shmooze" and get an agreed order in to either buy you some time to make up the arrears, or work out another deal with the lender.